The exact steady-state solution of a class of non-linear stochastic systems

1982 ◽  
Vol 17 (3) ◽  
pp. 137-142 ◽  
Author(s):  
T.K. Caughey ◽  
Fai Ma
Keyword(s):  
Steady State ◽  
Stochastic Systems ◽  
Steady State Solution ◽  
State Solution ◽  
Linear Stochastic Systems ◽  
Non Linear

A non-linear equation incorporating damping and dispersion

1970 ◽  
Vol 42 (1) ◽  
pp. 49-60 ◽  
Author(s):  
R. S. Johnson
Keyword(s):  
Steady State ◽  
Asymptotic Solution ◽  
Linear Equation ◽  
Numerical Integration ◽  
Phase Plane ◽  
Steady State Solution ◽  
State Solution ◽  
Averaging Technique ◽  
Non Linear Equation ◽  
Non Linear

The steady-state solution of the non-linear equation \[ h_t + hh_x + h_{xxx} = \delta h_{xx} \] with both damping and dispersion is examined in the phase plane. For small damping an averaging technique is used to obtain an oscillatory asymptotic solution. This solution becomes invalid as the period of the oscillation approaches infinity, and is matched to a straightforward expansion solution. The results obtained are compared with a numerical integration of the equation.

The stochastic observability for noisy non-linear stochastic systems†

1975 ◽  
Vol 22 (4) ◽  
pp. 461-480 ◽  
Author(s):  
YOSHIFUMI SUNAHARA ◽  
SHIN'ICHl AIHARA ◽  
MASAYUKI SHIRAIWA
Keyword(s):  
Stochastic Systems ◽  
Linear Stochastic Systems ◽  
Non Linear

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

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